Additions to the MAT 240 web site no longer count towards good deed points

#

Week of...

Notes and Links

1

Sep 7

Tue, About, Thu

2

Sep 14

Tue, HW1, HW1 Solution, Thu

3

Sep 21

Tue, HW2, HW2 Solution, Thu, Photo

4

Sep 28

Tue, HW3, HW3 Solution, Thu

5

Oct 5

Tue, HW4, HW4 Solution, Thu,

6

Oct 12

Tue, Thu

7

Oct 19

Tue, HW5, HW5 Solution, Term Test on Thu

8

Oct 26

Tue, Why LinAlg?, HW6, HW6 Solution, Thu

9

Nov 2

Tue, MIT LinAlg, Thu

10

Nov 9

Tue, HW7, HW7 Solution Thu

11

Nov 16

Tue, HW8, HW8 Solution, Thu

12

Nov 23

Tue, HW9, HW9 Solution, Thu

13

Nov 30

Tue, On the final, Thu

S

Dec 7

Office Hours

F

Dec 14

Final on Dec 16

To Do List

The Algebra Song!

Register of Good Deeds

Misplaced Material

Add your name / see who's in!


A complete set of the December 1st lecture notes given by Professor Dror BarNatan for the Fall Session of MAT240 at the University of Toronto.
~In the above gallery, there is a complete copy of notes for the lecture given on December 1st by Professor Natan (in PDF format).
 Wiki Format 
MAT240 – December 1st
Basic Properties of $\det :\mathbb {M} _{n\times n}\rightarrow F$:
(Note that det(EA) = det(E)·det(A) and that det(A) may be written as A.)
0. $\,\!\det(I)=1$
1. $\det(E_{i,j}^{1}A)=\det(A);E_{i,j}^{1}=1$
 Exchanging two rows flips the sign.
2. $\det(E_{i,c}^{2}A)=c\cdot \det(A);E_{i,c}^{2}=c$
 These are "enough"!
3. $\det(E_{i,j,c}^{3}A)=\det(A);E_{i,j,c}^{3}=1$
 Adding a multiple of one row to another does not change the determinant.
The determinant of any matrix can be calculated using the properties above.
Theorem:
If ${\det }':\mathbb {M} _{n\times n}\rightarrow F$ satisfies properties 03 above, then $\det '=\det$
$\det(A)=\det '(A)$
Philosophical remark: Why not begin our inquiry with the properties above?
We must find an implied need for their use; thus, we must know whether a function $\det$ exists first.